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Classifications

B01D3/00—Distillation or related exchange processes in which liquids are contacted with gaseous media, e.g. stripping

B01D3/42—Regulation; Control

B01D3/4211—Regulation; Control of columns

B01D3/425—Head-, bottom- and feed stream

G—PHYSICS

G05—CONTROLLING; REGULATING

G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS

G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion

G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric

G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators

G05B13/048—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators using a predictor

Description

The invention relates to a method according to the
Preamble of claim 1 (GB-Z- "Automatica", Volume 11, 1975, pp. 119-127). Also concerns the
Invention a control system for performing this method.

The field of application of the invention is virtually unlimited.
For example, it can be used in such different areas
like aeronautics, electrical engineering or
use chemical engineering.

Examples of processes in which the process according to
Invention has been applied is the single regulation
Input variable and a single output variable at
an airplane where the angle of climb is due to the elevator position
is regulated, and the multivariable scheme
a distillation column in which the compositions
at the top and bottom by the reflux and
the steam flow rates are regulated.

It is known that the control process of a system
with a control structure based on constant parameters
deteriorates when the dynamic parameters
of the process in an unforeseen way that
cannot be measured directly or indirectly.

In previous years, control techniques were developed
trying to solve this problem.

The most notable of these were based on adaptive systems theory
with model reference, which is basically based on a
of the following two types worked:

(1) It becomes a real-time adaptive estimate of the parameters
and state variables of the process executed from the one
adaptive controller calculates the control to be used in the process,
or

(2) it becomes the regulation to be applied in the process over a
adaptive control scheme calculated to the process output
to follow a model reference output.
In general, the rule structure in both requires above
executed cases, the planning of a correction facility.
The difficulties in calculating the
Parameters of this correction device occur increase
according to the scale of the process and limit
the scope of these known techniques very much.

Procedures using the conventional control loop principle
where the difference between the
Permanent state setpoint and the current process output vector
is evaluated, for example, the DE-Z "control technology
and process data processing ", 1972, pages 190-198,
from DE-Z- "Regelstechnik", 1976, pages 24-27, from Z- "Control",
May 1965, pages 253-258, from U.S. Patent 37 95 799 and out
GB-Z- "Automatica", Volume 8, 1972, pages 143-151.

This differs from this known principle in "Control Engineering"
May 1968, pages 75-78 specified concept. In this reference
However, it will only be a desired result and not a
Methods of achieving the same are described. That in this
Literature contained basic concept consists in
the desirability of a command signal depending
to generate from a predicted system output signal
but not in specifying a path like an actual one
System output signal can be formed. It essentially does
found that "everything is still about the applications of the
Technology has to be learned and experienced because technology
high-speed prediction control has not yet been developed
except in preliminary embodiments.
The formal theory of the Ziebolz controller has yet to be created
will".

From GB-Z- "Automatica", Volume 11, 1975, pages 119-127
one based on the prior art in the preamble of claim 1
Regulatory procedure known, in which the
controlling manipulated variable signal by considering a
Target process output vector is generated. This target process output vector
corresponds to that in the current moment
present target process output vector, i. H. the setpoint,
the process output signal already at the current time
should have. A future setpoint of the process output signal
is not considered in any way.
As with all other known regulatory procedures, too
in this procedure the fact that the regulation
process not immediately related to changes in the manipulated variable vector
appeals. Rather, it claims one beforehand
certain period of time to be regulated by the particular one
The process depends on the change in the manipulated variable vector
appeals, which then becomes a consequence of this
Change of the process input vector leads.

The object of the invention is a method for production
of a manipulated variable vector of a control process that
not the ones with more extensive correction facilities
resulting difficulties and in which the regulatory process
nevertheless almost immediately on changes of the
Manipulated variable vector.

This task is performed according to a generic method
the invention by the in the characterizing part of the claim
1 specified features solved.

Advantageous further developments of this method are in the
Claims 2 to 9 specified.

A convenient and advantageous control system for implementation
of the method according to the invention is in the claim
10 specified.

The following is a more general description of the embodiment of the invention
Regarding be described with reference to the accompanying figures.
Following this, the results of a special application
of the method according to the invention and a control system
demonstrated to perform this procedure.

Fig. 1 shows the general block structure of a control system for performing the method according to the invention;

Fig. 2 shows a distillation column in which a control system for performing the method according to the invention is used, so that a multivariable control of the compositions can be carried out at the upper end and at the bottom as output variables with reflux and steam flow rates as input variables;

Fig. 3 shows the results of such an application of a control system for implementing the method according to the invention in a distillation column in a graphical representation.

Two operating modes of a control system for carrying out the method according to the invention are possible in a scanning instant k , which is shown with reference to FIG. 1.

1. Via path 1 , a human or automatic operator 2 can directly set the control vector u(k) , which represents the input variable for a device 3 and an identification block 4 for a scanning instant k . The identification block 4 contains an adaptive-predictive model 5 for calculating an estimated process output vector d(k) . The error e(k) of this estimate, ie the difference between the process output vector y(k) and d(k) , is used to update the parameters of the aforementioned adaptive-predictive model 5 via an adaptive mechanism 6 . This mode of operation is to be referred to as the identification mode of operation.

2. Via path 7 , the parameters of the adaptive-predictive model 5 , as previously described, are brought up to date. Is beyond but in the process applied is calculated by a control block 8, in which the same adaptive-predictive model is used such that the desired output vector of the process d ₁ (k + r + 1) k in the sampling instant + r + 1 corresponds to the predicted output vector for the same instant k + r + 1, r is the number of sampling time delays observed in the process or considered to be appropriate. d ₁ (k + r + 1) is calculated at the moment k by a driver block 9 in response to the input variables of the operator 2 . This mode of operation is to be referred to as the standard mode of operation.

The adaptive-predictive control system always uses value changes (increment values) of the output variable, the input variable and of measurable interference vectors of the process to carry out the process control. If desired, the rule vector can be kept at a limit. The specific operations which the control system carries out with the aid of a digital computer at each sampling instant k during its control mode of operation, thus taking into account the concept described above, are explained below:

a) measurement and, if considered appropriate, filtering the output variables of the process in order to obtain the process output vector yp(k) . Its dimension should be viewed as n .

Herein, up(k - i - r) and wp(k - i - r ₂) are the control vector and the measurable interference vector in the dimensions n ₁ and m at the sampling time k - i - r and k - i - r, respectively ₂. In equation 2, the integers h, f and g can be chosen appropriately. Similarly, the integers r ₁ and r ₂ can be chosen appropriately, taking into account the available or predicted measurements of the output and interference vectors. The matrices Ai(k - 1), Bi(k - 1) and Ci(k - 1) of the adaptive-predictive model have their own dimensions and their values correspond to a past value before they were brought up to date k were. If the dimension of the rule vector is larger than the dimension of the output vector, then in most cases additional conditions should be added to achieve a single rule solution or some of the rule vector components can simply be included in the interference vector. The case n ₁ = n is regarded as a special case.

e) Calculation of the updated values at the time k of the parameters aÿq(k) , bÿq(k) and cÿq(k) , which are the elements in the j- th row and q- th column of the matrices Ai(k) , Bi(k) and Ci(k) are, using the following algorithms: aÿq(k) = baÿqαj(k)ej(k)yq(kir ₁) + aÿq(k -1) (Eq. 6) bÿq(k) = βbÿqαj(k)ej(k)uq(kir) + bÿq(k -1) (Eq. 7) cÿq( k) = βcÿqαj(k)ej(k)wq(kir ₂) + cÿq(k -1) (Eq. 8) Here are ej(k) , yq(kir ₁), uq(kir) and wq(kir ₂) each have the corresponding components of the vectors e(k) , y(kir ₁), u(kir) and w(kir ₂). βaÿq , βbÿq and βcÿq are coefficients that can be matched appropriately, and αi(k)(j = 1, n) are different gains that can be easily selected in the wide range of possibilities using the known gradient parameter identification technique allowed. A particular choice of these variable reinforcements can be the following:

f) calculation of the desired incremental output vector d ₁ (k + r +1), which can be carried out by the driver block as follows:

1. Calculation of the desired process output vector dp(k + r +1) of the dimension (nx 1), which can be carried out in various ways by using a model reference with the desired dynamics or any other plan that contains the desired dynamics and also the previously measured or predicted process output variables are taken into account. The latter type of plan can be z. For example, define using the following equation: Herein, y(k + r + 1- r ₁- i) and v(k + 1- i) are the process output vector and the driver block input vector at the sampling moment k + r + 1- i and k + 1- i, respectively. v(k +1+ i) is a vector of dimension n that is generated directly by the operator. The matrices Fi(i = 1, t) and Hj(j = 1, s) can be freely selected in the same way as the integers t and s , taking into account the desired dynamics.

2. From the value of the desired output vector of the process dp(k + r +1), the desired incremental output vector d ₁ (k + r +1) can be calculated in various ways without difficulty. A special type, which is suitable if γ < r , is given by the following equation: d ₁ (k + r +1) = dp(k + r +1) - yp(k + r + 1- γ ) (Eq. 11) If it has been found necessary, the value of d ₁ (k + r +1) can be kept at a limit.

g) calculation of the rule vector according to the following:

1. From the updated adaptive-predictive model, the predicted incremental process output vector d ₁ ' (k + r +1) depends on the sampling instant k + r +1 from the incremental control vector u(k) and is given by the following equation : (k + r +1) equals the desired incremental output variable d ₁ (k + r +1), and is given by the following equation:

h) If desired, the control vector up(k) can be kept at a limit value before it is fed into the process.

In its execution, the adaptive-predictive control system
incremental input, output and interference vectors
use as it does in the above modes of action
has been described. Another way of system execution
but consists in calculating the incremental
Input, output and interference vectors with respect to
some constant, suitably chosen vectors. As a result
must be in the equations below the equation numbers
1, 3, 4, 11 and 14, the following, respectively
Changes are made:

y(k) = yp(k) - ypc (Eq. 15)

u(kir) = up(kir) - upc (Eq. 16)

w(ki-r₂) = wp(ki-r₂) - wpc (Eq. 17)

d ₁ (k + r +1) = dp(k + r +1) - ypc (Eq. 18)

up(k) = u(k) + upc (Eq. 19)

If it is considered appropriate to give specific values to some of the adaptive-predictive model parameters (e.g. due to a certain process knowledge), these values can also be given to the respective parameters and the corresponding β coefficients are set to zero. It is also possible to stop those adaptive-predictive model parameter operations that are brought up to date for as long as is considered appropriate.

If the system works in identification mode, needs
it only performs operations a through e. These
Identification activity can be in real-time operation or
in off-line operation and even in operation between the
Sampling intervals are performed.

It can be observed that in operation g to calculate u(k) the matrix B 1 (k) must be inverted. The risk of a singularity of the matrix B ₁ (k) can in practice almost always be avoided by adding time delays to the process input and output vector and by regulating the resulting process. An illustrative experimental example of this procedure is presented in this patent application.

Another way to implement the control system is to bring the adaptive-predictive model into such a form that the vector d(k) is not the estimate of the vector y(k) but the estimate of any other output or input vector in a previous sampling instant. The error in this estimate is used to bring the adaptive-predictive model up to date.

In some cases, an equivalent way of using the control system shown here is to break it down into a set of systems with a single output and multiple inputs, each of which is subject to a condition that is checked by the component of the control vector at each sampling instant. The rule vector for each sampling instant can be calculated from the set of n corresponding linear equations.

Finally, the static reinforcements of the process
by multiplying the components of its output, input
and interference vectors or the incremental vectors
be modified with scalar gains. Also the
Dynamic process can be done in an analog way
be modified. In this case the control system
the process by regulating the modified process
regulate.

The adaptive-predictive control system described earlier
is for multivariable regulation of the compositions
(in percent by weight of methanol) at the top and at
Bottom of a binary distillation column,
namely at the Chemical Engineering Department, University
from Alberta, Edmonton, Alberta (Canada).

As shown in Fig. 2, a feed flow 11 enters the distillation column 10 at the fourth ash container. The product from the top of the distillation column condenses in a device 12 through cooling water and falls into a container 13 . The aim of the experiment shown here is to regulate the composition of the bottom product 15 which goes away from the bottom of the column.

The reflux rate 16 and the steam flow rate 17 , which heats a reheat boiler 18 at the bottom of the column, were used as control variables. To complete the experiment, a digital computer 19 was used, to which the measurements made by a composition registration device 20 and a gas chromatograph 21 of the compositions present at the top and bottom were entered, and which regulates the setting variable of two flow registration controllers 22 and 23 . In addition, the column also has the following devices: two liquid level display controllers 24 , two flow registration devices 25 , a pressure display controller 26 , two temperature registration controllers 27 and a flow registration controller 28 .

The control variables are the reflux and steam flow rates.
The sampling period is 256 sec. Because of this
large sampling period there is no time delay between
the composition at the top and the reflux
and steam flow rates. There is a measurement time delay
of a sampling period between the soil composition
and the steam flow rate due to the analysis time,
which are required to measure the soil composition
is. Between the soil composition and the reflux rate,
it was found that there are two sampling intervals.
There was no significant disruption to the process.

To avoid the problem of the singularity of B ₁ (k) , which was previously discussed, a sampling time delay is added to measure the composition at the top. Accordingly, the corresponding component of the process output vector with respect to the top composition at sampling time k is the measurement of the top composition at time k -1. This component at the moment k +1 is also known at the moment k .

According to the circumstances described above, at each sampling time k, the sequence of operations performed by the adaptive-predictive control system during its control activity is:

1. Measurement of the top and bottom compositions to obtain the process output vector yp(k) , the components of which are the top composition yp(k) measured at time k -1 and the bottom composition yp 2(k) measured at time k .

2. The number of sampling time delays r considered for the process is equal to 1 in this case and the integer y was chosen equal to 2. Accordingly, the incremental output vector is calculated by: y(k) = yp(k) - yp(k -2) (Eq. 20)

3. In the adaptive-predictive model, the integers h , f and r ₁ were chosen equal to 3, 4 and 0; there was no interference vector. As a result, the estimated incremental output vector d(k) was calculated by: Herein, d 1 and y 1 are the components with respect to the above composition. d ₂ and y ₂ are the components in terms of soil composition. u ₁ and u ₂ are the incremental reflux or steam flow rates. The incremental rule vector u(ki -1) is obtained by: u(ki -1) = up(ki -1) - up(ki -3) (Eq. 22) Here up(ki -1) is the rule vector present at time ki -1. The matrices Ai(k -1) (i = 1, 3) and Bi(k -1) (i = 1, 4) are chosen as follows:

4. Calculate the estimation error vector as used in the equation
5 is displayed.

5. Calculation of the updated values at the moment k from the parameters of the matrices Ai(k)(i = 1, 3) and Bi(i = 1, 4) according to equations 6, 7 and 9, where it is taken into account that no disturbances are considered, that the value of the coefficients β corresponding to the non-zero parameters in the top and bottom rows were set to 1 and 0.1, respectively, and that the coefficients β ' corresponding to the remaining zero parameters both were set to zero in the top and bottom rows.

6. The components dp 1(k +2) and dp 2(k +2) of the desired process output vector dp(k + +2) relating to the top and bottom compositions at the time k +2 are given by the following scale equations calculated which are a special case of equation 10: Herein, v ₁ (k + 1- i) and v ₂ (k + 1- i) are the components with respect to the top and bottom compositions of the driver block input vector v(k + 1- i) at the time k + 1- i . The parameters of equations 23 and 24 were chosen to be the same as those of a second-order model, with or without a sampling time delay, a natural frequency of 0.0056 rad / sec. and a damping ratio and a static gain equal to 1. Provided that the value of the aforementioned static gain is one, the components v ₁ (k + 1- i) and v ₂ (k + 1- i) have the physical meaning to be the manipulated variable values for the top and bottom compositions at the time k + 1- i . In equation 23, the value y ₁ (k +1) was previously calculated by: y ₁ (k +1) = yp 1(k +1) - yp 1(k -1) (Eq. 25) determine that yp(k +1) is the value of the top composition measured at the moment k . From dp(k +2) the desired incremental process output vector d ₁ (k +2) is calculated by: d ₁ (k +2) = dp(k +2) - yp(k) (Eq. 26) Die components d ₁₁ (k +2) and d ₁₂ (k +2) of d ₁ (k +2) related to the top and bottom compositions are limited to the absolute values 0.3 and 0.6%, respectively.

7. Calculation of the rule vector by:

8. The absolute and the incremental value of up(k) is kept before the process is fed.

Fig. 3 shows the results of a six hour and 24 minute test from the beginning, the distillation column being controlled by the adaptive-predictive control system.

In Fig. 3, the graphs A, B, C and D on the Y axis represent the top composition (%), the bottom composition (%), the reflux rate (g / sec) and the steam flow rate (g / sec ) depending on the time plotted on the X axis in sampling times.

The initial values of the parameters of the adaptive-predictive
Models were chosen sensibly. The control system worked
before entering regular activity for two
Sampling times in its identification mode. As soon as
control begins, drives the control system
the top and bottom compositions of the process of
96.5 or 1% to 96 or 3%. Later, at time 29,
while keeping the soil composition at 3%,
the top composition is driven to 97%. To the
At point 55 the soil composition will change from 3 to 5%
driven and the top composition kept at 97%.

It should be noted that the multivariable control problem
a binary distillation column, which by the
adaptive-predictive control system according to the invention in
to be recommended, often for a long time
mentioned example of difficulties in influencing each other
multivariable chemical processes
is.

Claims (10)

1. A method for generating a manipulated variable vector during each of a plurality of sampling times, each separated by a constant time interval, which is fed to an apparatus which carries out a process having at least one input variable and at least one output variable, at least one of the input variables defining a process output vector and the Apparatus this process output vector varies depending on the value of the manipulated variable vector using a stored model that predicts the manner in which the control process responds to changes in the manipulated variable vector and generates a manipulated variable vector as a function thereof, characterized in that the model has the dynamic value a process output vector consisting of at least one of the process output variables at a future sampling time k + r +1 as a function of the manipulated variable vector, where k predicts the current n currently occurring sampling time and r represents the number of sampling intervals that is required to respond to the control process to a change in the manipulated variable vector, that at each of the sampling times k a dynamic target process output vector is generated, which is representative of a target value of the process output vector at the future sampling time k + r +1, and that in each of the sampling times k the manipulated variable vector is generated which the model predicted and which causes the dynamic process output vector to become equal to the dynamic target process output vector at the future sampling time k + r +1.

2. The method according to claim 1, characterized in that
taking into account the dynamic target process output vector
the desired dynamics of the process and as a function
both the target steady state process output vector
and the dynamic process output vector is formed.

3. The method according to claim 1 or 2, characterized in
that the generation of the dynamic target process output vector
the generation of an incremental dynamic target
output vector that is representative of the incremental
Difference between the dynamic target process output vector
and the dynamic process output vector
is.

4. The method according to any one of the preceding claims, characterized
characterized in that the manipulated variable vector is an incremental
The manipulated variable vector is representative of the incremental
Change of the process input vector is, which according to
the prediction of the model.

5. The method according to any one of the preceding claims, characterized in that the parameters of the model are periodically updated so that the difference between the actual dynamic process output vector at the time k + r +1 and that of the model for the time k + r +1 predicted dynamic process output vector is reduced to zero.

6. The method according to claim 5, characterized in that the updating of the model comprises the following steps:

a) Periodically generating an estimated process output vector representative of a dynamic process output vector which the model, after being updated during a first predetermined sampling time, estimates that it will be at a sampling time k as a result of the generation of the Control variable vector occurs at the earlier sampling time kr -1;

b) periodically generating an estimated error vector representative of the difference between the estimated process output vector at sampling time k and the dynamic process output vector at sampling time k ;

c) Periodically changing the parameters of the model as a function of the estimated error vector.

7. The method according to claim 6, characterized in that additionally the generation of an incremental process output vector is provided, which is representative of the difference between the actual dynamic process output vector at time k and the actual dynamic process output vector at a second, earlier sampling time.

8. The method according to claim 7, characterized in that
that the estimated process output vector is that estimated by the model
Value of the incremental dynamic process output vector
is after the model at the first one in front
Sampling time was updated.

9. The method according to claim 8, characterized in that the
Generating an estimated error vector the determination
the difference between the incremental process output vector
and the estimated process output vector.

10. Control system for performing the method according to one of the preceding claims, characterized in that a driver block ( 9 ) is provided which has an input specification vector (setpoint vector) v(k) and an instantaneous process output vector yp(k) for generating an incremental setpoint process output vector d ₁ (k + r + 1) k receiving during each of a plurality of sample, wherein the incremental target process output vector d ₁ (k + r + 1) of the incremental target change between the sampling time k and the sampling instant k + r + 1 corresponds to that a control block ( 8 ) is provided, which records the incremental target process output vector d ₁ (k + r +1) for generating an incremental control variable vectoru(k) during each of the sampling times k according to an adaptive-predictive model ( 5 ), wherein the adaptive-predictive model serves to predict the process output vector and to determine the incremental manipulated variable vector u(k) , de r must be supplied to the process during the sampling time k in order to make the predicted process output vector equal to the target process output vector during the sampling time k + r +1, which is determined by the incremental target process output vector d 1 (k + r +1), that an identification block ( 4 ) is provided, which records the incremental manipulated variable vector u(k) and an incremental process output vector y(k) for generating an estimated incremental process output vector d(k) during each of the sampling times k according to the adaptive-predictive model ( 5 ) wherein the estimated incremental process output vector d(k) representative of the incremental process output vector to the adaptive-predictive model, after it has been brought to a k before the sampling past sampling time to the latest predicts and k during time as a result the generation of the incremental manipulated variable vector u(kr -1) should occur during the sampling instant kr -1 that means for generating an estimated error vector e(k) is provided during each of the sampling instants k , the estimated error vector e(k) being representative of the difference between the estimated incremental process output vector d(k) and the incremental process output vector is y(k) , and that a feedback taking the estimated error vector e(k) is provided for changing the parameters of the adaptive-predictive model ( 5 ) during each of the sampling times k , the parameters of the adaptive -predictive model can be changed such that the estimated error vector e(k) is reduced to the value zero.